If you can get within 20 to 30 feet of the action, you can do it for $600 if you do some careful shopping.
You need a DSLR (digital single lens reflex) camera and a bright lens.
Look at the Canon 350D, Nikon D50 or D40.
You want to get the camera without a lens.
Buy a 50mm f1.8 lens. The lens will cost under $100.
I am looking for a camera that will take good pictures indoors without a flash, specifically for gymnastics meets. I currently have a digital camera that is 5 years old and all the pictures are dark. I do not know anything about cameras but I am willing to learn and take a few classes if necessary. I would like to spend about $600 but if I need to spend more I will. I would also like to have a camera that doesn't not have a lot of lag time from when I push the button to when the picture is actually taken. I am sorry I do not know what this is called, it definitely shows my ignorance. The stores I have gone into have not been much help. Any assistance would be appreciated. Thanks.